Many forms of information can be described as a set of objects, each with a set of attributes and/or values. In these cases, any hierarchical structure remains implicit. Often the set of objects can be related to two or more completely different domains of attributes and/or values. Formal Concept Analysis (FCA) is a principled way of deriving a partial order on a set of objects each defined by a set of attributes. It is a technique in data and knowledge processing that has applications in data visualization, data mining, information retrieval, and knowledge management (see the List of Incorporated Cited Literature References, Literature Reference No. 2). The principle with which it organizes data is a partial order induced by an inclusion relation between object's attributes. Additionally, FCA admits rule mining from structured data.
Neural decoding is a neuroscience-related field concerned with the reconstruction of sensory and other stimuli from information that has already been encoded and represented in the brain by networks of neurons. Prior art in methods for neural decoding have used machine learning algorithms for classification. Examples include support vector machines for electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) (see Literature Reference No. 6). Neural decoding methods that don't specifically classify but parameterize data in the stimulus domain include multivariate parametric analysis, of which a common subset is regression methods. Prominent examples of the state-of-the-art using regression methods are in fMRI (see Literature Reference No. 7). This prior art treats each voxel (fMRI blood-oxygen-level-dependent (BOLD)) independently and parameterizes its response according to variables (stimulus space) defined a priori. In essence, any structure in the neural data can only relate directly to the explicit structure as defined in the variables a priori, forming an activation map for these variables. Thus, hierarchical relationships implicit in the neural data in a regression framework are treated as independent variables (i.e., flat), even if the stimulus variables have explicit hierarchy. Other prior art takes words from a corpus of articles to produce topics from statistical distributions of words; however, it also flattens any hierarchies by simply regressing the neural data onto topics (see Literature Reference No. 8).
Thus, a continuing need exists for a system that seeks to first discover hierarchical structure in the neural data, and relate it to structure in the variables, or stimulus space.